Hello! Can someone please help me with this?

I need to calculate the following integral by principle, that means resolving the limit of the sum.

The integration segment [0,T] is partitioned in N partitions of size T/N.

$\displaystyle

\int_0^{T} x^4\ dx\ = \lim_{N\to \infty}\sum_{i=0}^{N-1} x_{i}^{4}(x_{i+1} - x_{i})

$

Thanks a bunch!